Abstract
A simple variational property concerning the velocity distribution of a set of point particles is illustrated. This property provides a full characterization of the velocity distribution which minimizes the kinetic energy of the system for prescribed values of linear and angular momentum. Such a characterization is applied to discuss the kinetic energy dissipation in the sticking collision of free rigid bodies. Special cases are also examined where not all the components of linear and angular momentum are conserved, corresponding to rigid bodies with a common fixed point or axis without friction. As a byproduct, a formal property of the tensor of inertia is derived, not commonly considered in mechanics textbooks. Along with the variational property of the velocity distribution, such a formal property of the tensor of inertia may be interesting for graduate and advanced undergraduate students.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
